The New York Times ran a story on Sunday claiming some celebrities and their publicists are upset that the magazine has toughened its coverage on Hollywood and its stars.

The piece cited recent examples in the magazine about Brad Pitt’s "World War Z" production disaster and the effect of Scientology on Tom Cruise and Katie Holmes’ marriage.

In May, Gwyneth Paltrow willingly appeared on the covers of People and Good Housekeeping — but refused to cooperate with Vanity Fair.

In an email obtained by the Times, Paltrow allegedly wrote to friends at the time:

“Vanity Fair is threatening to put me on the cover of their magazine. If you are asked for quotes or comments, please decline. Also, I recommend you all never do this magazine again.”

Carter released this statement in response to reports about Paltrow and her posse boycotting the mag:

“We wouldn’t be doing our job if there wasn’t a little bit of tension between Vanity Fair and its subjects. In any given week, I can expect to hear from a disgruntled subject in Hollywood, Washington, or on Wall Street. That’s the nature of the beast.”

It's a bold move for Paltrow, as editor Graydon Carter is an influential force in the industry. Not to mention, he hosts the Vanity Fair post-Oscar party — Hollywood's hottest party of the year.

Cindy Ord/GettyGraydon Carter says “We wouldn’t be doing our job if there wasn’t a little bit of tension between Vanity Fair and its subjects."

But it may not matter anymore, as the Times notes, "Celebrities and their publicists can now circumvent traditional media outlets and communicate with their fans directly through Twitter and Facebook."

Leslee Dart, a publicist whose clients include Tom Hanks, Woody Allen and Meryl Streep, agrees, telling the paper, “I don’t think people care the way they used to anymore. It’s not important to them to grovel as they once did. Magazines are less relevant.”

Other big Hollywood players disagree.

“Vanity Fair’s influence is still enormous,” Ron Meyer, president of Universal Studios, told the Times, while Harvey Weinstein said a mention in its pages was “the Good Housekeeping seal of approval in the media world” for a movie.

So who needs whom more?

Well, Vanity Fair's newsstand sales have declined 32.9% in the last five years, though that is better than the industry average of 39%, according to the Alliance for Audited Media.

In July, the Vanity Fair Web site had 1.2 million unique visitors, reports the Times.

Gwyneth Paltrow, meanwhile, has 1,726,872 Twitter followers alone — not to mention the circulation of her popular weekly digital media and e-commerce newsletter, Goop.